Class Of Problems Research Articles

On smoothness conditions and selection of the edge of a scattering surface in one class of 3D time-optimal problems

A class of time-optimal problems in three-dimensional space with a spherical velocity vectogram is considered. The target set is a parametrically defined smooth curve. Numerical and analytical approaches to constructing the bisector of the target set — the scattering surface — in the time-optimal problem are proposed. The algorithms are based on formulas for the edge points of the scattering surface, written in terms of curve invariants. It is shown that these points form the edge of the bisector and lie at the centers of the touching spheres to the curve. A theorem on sufficient conditions for the smoothness of a scattering surface is proven. The equations of the tangent plane to the bisector are found for those points from which exactly two optimal trajectories emerge. An example of solving a time-optimal problem in the form of a set of level surfaces of the optimal result function is given, highlighting the surface of their non-smoothness.

A solution to the only one object problem with dissolution rules

In the framework of membrane computing, (non-)uniform families of recognizer membrane systems are usually defined to solve abstract decision problems. In this sense, the use of finite resources for each member of the family makes the difference with respect to Turing machines solving these problems. While keeping the finite nature of these systems, it is interesting to know which type of problems can be solved by means of a single membrane system. For this purpose, the complexity class PMCR1p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{PMC}^{1p}_{\\mathcal {R}}$$\\end{document} was defined as the class of problems that can be solved by means of a single membrane system in polynomial time. Due to the polynomial-time encoding of the input, at least all the problems from P can be solved with a trivial system. To go below P, the class PMCR1f\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{PMC}^{1f}_{\\mathcal {R}}$$\\end{document} restricts the definition of this encoding. In this work, we study the capability of different types of membrane systems to solve the ONLY-ONE-OBJECT problem, while having the encoding restriction.

Probabilistic zero bounds of certain random polynomials

Abstract This paper introduces the notion of probabilistic zero bounds for random polynomials. It presents new results regarding the probabilistic bounds of random polynomials whose coefficients are independently and identically distributed as standard normal variates. Additionally, the paper provides a clear exposition of the developed methodology. To establish our results, we develop a novel approach utilizing the classical Cauchy’s bounds for the zeros of a deterministic polynomial with complex coefficients. We also corroborate our analytical results with extensive simulations. The methodology developed in the paper can potentially be applied to a broad class of problems regarding bounds and the distribution of zeros in the theory of random polynomials.

Informed Adaptive Sensing.

For many inverse problems, the data on which the solution is based is acquired sequentially. We present an approach to the solution of such inverse problems where a sensor can be directed (or otherwise reconfigured on the fly) to acquire a particular measurement. An example problem is magnetic resonance image reconstruction. We use an estimate of mutual information derived from an empirical conditional distribution provided by a generative model to guide our measurement acquisition given measurements acquired so far. The conditionally generated data is a set of samples which are representative of the plausible solutions that satisfy the acquired measurements. We present experiments on toy and real world data sets. We focus on image data but we demonstrate that the method is applicable to a broader class of problems. We also show how a learned model such as a deep neural network can be leveraged to allow generalisation to unseen data. Our informed adaptive sensing method outperforms random sampling, variance based sampling, sparsity based methods, and compressed sensing.

Resources of curriculum materials that induce teachers' professional knowledge of the additive conceptual field

Assuming that curriculum materials reverberate the knowledge of teachers, we sought to identify and discuss features of the materials, related to the additive field, which induce professional knowledge in Mathematics. Through a documentary analysis of three 2nd, 3rd and 4th grade Mathematics Teacher's Manuals, the addition and subtraction problems were mapped and analyzed; the texts presenting the material and the units corresponding to the mapped problems were analyzed, as well as the specific guidelines for working with these problems. Considering the Conceptual Fields Theory and the Knowledge of Knowledge of Curriculum Embedded Mathematics as references, we identified a variety of problem classes, as well as guidelines on the different meanings of operations. We observed weaknesses in the approach taken in the 2nd grade Manual corresponding to the addition and subtraction approach, to the detriment of the other Manuals. We noted the absence of explicitly stated information in the three manuals, which may have an impact on the way teachers read and interpret the guidelines, and evaluate the problems, implying the teaching knowledge mobilized or constructed.

Input Regularization for Integer Optimal Control in BV with Applications to Control of Poroelastic and Poroviscoelastic Systems

We revisit a class of integer optimal control problems for which a trust-region method has been proposed and analyzed in arXiv:2106.13453v3 [math.OC]. While the algorithm proposed in arXiv:2106.13453v3 [math.OC] successfully solves the class of optimization problems under consideration, its convergence analysis requires restrictive regularity assumptions. There are many examples of integer optimal control problems involving partial differential equations where these regularity assumptions are not satisfied. In this article we provide a way to bypass the restrictive regularity assumptions by introducing an additional partial regularization of the control inputs by means of mollification and proving a $\Gamma$-convergence-type result when the support parameter of the mollification is driven to zero. We highlight the applicability of this theory in the case of fluid flows through deformable porous media equations that arise in biomechanics. We show that the regularity assumptions are violated in the case of poro-visco-elastic systems, and thus one needs to use the regularization of the control input introduced in this article. Associated numerical results show that while the homotopy can help to find better objective values and points of lower instationarity, the practical performance of the algorithm without the input regularization may be on par with the homotopy.

Existence and regularity results for a class of singular parabolic problems with L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1$$\\end{document} data

In this paper we prove existence and regularity results for a class of parabolic problems with irregular initial data and lower order terms singular with respect to the solution. We prove that, even if the initial datum is not bounded but only in L1(Ω)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1(\\Omega )$$\\end{document}, there exists a solution that “instantly” becomes bounded. Moreover we study the behavior in time of these solutions showing that this class of problems admits global solutions which all have the same behavior in time independently of the size of the initial data.

Existence and multiplicity of nontrivial solutions to a class of elliptic Kirchhoff-Boussinesq type problems

Existence and multiplicity of nontrivial solutions to a class of elliptic Kirchhoff-Boussinesq type problems

Semilinear elliptic problems involving a fast increasing diffusion weight

In this work we study the existence and multiplicity of positive bounded solutions to a class of problems with a reaction–diffusion equation: −divK(x)∇u=f(x,u)inRN,u(x)→0as|x|→∞.Using a sublinear hypothesis on the nonlinearity f(x,u) near the origin, we obtain a solution u1. Furthermore taking K(x)=eθ(x) where θ(x) satisfies some fast increasing growth conditions, we find via variational methods, a second solution u2 in such a way that u2>u1. For this purpose, a new type of compactness is provided for the associated energy functional.

Uniqueness of solutions to some classes of anisotropic and isotropic curvature problems

In this paper, we apply various methods to establish the uniqueness of solutions to some classes of anisotropic and isotropic curvature problems. Firstly, by employing integral formulas derived by S. S. Chern [20], we obtain the uniqueness of smooth admissible solutions to a class of Orlicz-(Christoffel)-Minkowski problems. Secondly, inspired by Simon's uniqueness result [61], we then prove that the only smooth strictly convex solution to the following isotropic curvature problem(0.1)(Pk(W)Pl(W))1k−l=ψ(u,r)onSn must be an origin-centred sphere, where W=(∇2u+ug0), ∂1ψ≥0,∂2ψ≥0 and at least one of these inequalities is strict. As an application, we establish the uniqueness of solutions to the isotropic Gaussian-Minkowski problem. Finally, we derive the uniqueness result for the following isotropic Lp dual Minkowski problem(0.2)u1−prq−n−1det⁡(W)=1onSn, where −n−1<p≤−1 and n+1≤q≤n+12+14−(1+p)(n+1+p)n(n+2). This result utilizes the method developed by Ivaki and Milman [42] and generalizes a result due to Brendle, Choi and Daskalopoulos [10].

Existence of positive solutions to a class of boundary value problems with derivative dependence on the half-line

Existence of positive solutions to a class of boundary value problems with derivative dependence on the half-line

On the Bregman-proximal iterative algorithm for the monotone inclusion problem in Banach spaces

In this paper, we focus on the solution of a class of monotone inclusion problems in reflexive Banach spaces. To reflect the geometry of the space and the operator, a more general proximal point iterative algorithm with Bregman divergence is proposed and some strong convergence results for the proposed scheme under standard assumptions are obtained. Meanwhile, the convex optimization problems and the critical point problems are studied in the applications, and the recovery of the sparse signal is simulated in the numerical experiments.

Existence and uniqueness of Solution for Boundary Value Problem of Fractional Order

In this study, we investigate a class of fractional ordering and fractional derivative-based boundary value problems. and . There are four boundary value requirements in this equation. The Banach fixed point theorem (Contraction mapping theorem) and the Schauder fixed point theorem are both used to arrive at the existence and uniqueness solution. Examples based on the fractional integral method and integral operator are used to illustrate our main points.

STUDY OF MULTI-STAGE SOFTWARE DEPLOYMENT STRATEGYWITH THE EXCLUSION OF SIDE EFFECTS

The article addresses a problem and its solution that arose during onboarding of new subscribers to the existing data import and distribution service. The analysis of all available solutions demonstrates that none fully meet the requirements. The process of searching for the values of the required indicators and the process of creating reports necessarily uses indexes. Messages of different types are placed in their respective MongoDB collections. Over the long period of operation of the repository, up to 64 indexes per collection have accumulated. According to the policies of connecting to the storage (Connect timeout) and waiting for a response (Socket timeout), the need to set such long-time expectations for consumers is unacceptable and usually, by default, is equal to 30 seconds. A multi-step strategy for delivering the solution that allows the service to meet availability requirements was proposed. The novelty of the article is in the description and investigation of a new method of delivering solutions to the software deployment environment—production. The implementation of the described strategy opens a new approach for solving similar classes of problems related to the type of interaction with users, when custom settings are a mandatory part of the service and are guaranteed to carry the threat of service unavailability. This approach opens up new opportunities for achieving high availability of systems, reducing risks and increasing user satisfaction. Based on the analysis of the proposed approaches, the latest strategy of multi-step delivery of the service to users was developed, the result of which was the acceptable response waiting time of up to 5 seconds. The implementation of this strategy contributed to the achievement of the availability of software products - 99.999%, ensuring the reliability and stability of services for end users.

Differential evolutionary using opposition-based learning for multimodal multi-objective optimization

The correspondence between the decision space and the objective space is often many-to-one in multi-objective optimization problems. Therefore, a class of problems with such mapping relationships is defined as a MMOPs. For these problems, how to ensure the final solution converges to each Pareto solution set and guarantees the diversity of the algorithm is an urgent problem. The method of the paper with opposition-based strategy, a multimodal multi-objective optimization algorithm, is proposed. The algorithm proposed is called MMODE_OP, which is framed by a differential evolutionary algorithm, and opposition-based learning is applied to the initialization phase and generation-hopping phase to filter out the more promising individuals in the population for iteration to enhance the global search capability and the diversity of population. In addition, different Gaussian perturbation strategies are adopted with iteration to achieve the search of the neighborhood, which can further not only improve the quality of the Pareto solution set but also enable the convergence of the Pareto solution set quickly. This method improves the algorithm’s local and global search ability, and enables multiple the Pareto solution set and improving the convergence. In the meantime, adaptive scaling factors and crossover factors are designed in this paper to enhance the improved search capability. Finally, the experiment results of MMODE_OP and other excellent algorithms on 13 test problems corroborate the proposed methods have superior performance.

Guiding Fuzzy Cognitive Mapping With Structured Decision Making to Inform Complex Natural Resource Management Problems in Waiʻanae Hawaiʻi

AbstractFire is one example of a larger class of wicked environmental management problems that require community‐based management for long‐term success. This study aimed to support participatory decision making in a data poor and complex system by using Fuzzy Cognitive Mapping (FCM) within the decision‐making framework Structured Decision Making (SDM) to develop a community‐based wildfire management plan in partnership with a local group in Wai‘anae Hawaiʻi. SDM is an organized process to create and evaluate decisions that can clarify trade‐offs and increase transparency. FCM is a semi‐quantitative method to describe system relationships that can handle low data and high uncertainty. We used SDM to define the problem, articulate community concerns related to wildfire, and identify management actions. We then used FCM to model how these actions affected valued ecosystem services and other stakeholder‐identified objectives. Modeling results highlighted the trade‐offs across three valued ecosystem services from three community‐led wildfire management actions. We found that native species outplanting was the most beneficial action to each of the three valued ecosystem services. Through this participatory research, we conclude that the SDM and FCM pairing provided an inclusive and cost‐effective way to engage with a specific wildfire management context, and that the process effectively engaged stakeholders while tackling uncertainty. This process also aided consensus‐building and group member communication. This pairing can be used to aid community decision‐making across diverse management problems as it provides a way to elicit objectives and model trade‐offs, even under uncertainty and data limitations, while including stakeholders impacted by such decisions.

0718 Latent Classes of Sleep Problems and Subjective Cognitive Decline Among U.S. Middle-Aged and Older Adults

0718 Latent Classes of Sleep Problems and Subjective Cognitive Decline Among U.S. Middle-Aged and Older Adults

Formulating and heuristic solving of contact problems in hybrid data-driven computational mechanics

In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear optimization problem (NLP) rather than the much harder discrete-continuous NLP (DCNLP) of the direct DDCM approach. The key focus is on the addition of geometric inequality constraints to the hybrid DDCM formulation. Therein, the required constraint force leads to a contact problem in the form of a mathematical program with complementarity constraints (MPCC), a problem class that is still less complex than the DCNLP. For this MPCC we propose a heuristic quick-shot solution approach, which can produce verifiable solutions by solving up to four NLPs. We perform various numerical experiments on three different contact problems of increasing difficulty to demonstrate the potential and limitations of this approach.

Evolutionary simultaneous under and oversampling of instances for dealing with class-imbalance datasets in multilabel problems

Multilabel classification has recently attracted great attention from the data mining research community. Multilabel classification is concerned with learning where each instance can be associated with multiple classes (or labels). Class-imbalance problems appear in any classification task when the class distribution of the instances is very different. In multilabel classification, this problem is ubiquitous, as a large percentage of labels suffer from a class-imbalanced distribution. The adaptation of single-label methods to deal with the class-imbalance problem in multilabel learning is problematic as many of their basic concepts are not easily transferred. In this paper, we propose the use of evolutionary computation to simultaneously oversample the minority class and undersample the majority class for multilabel problems. Letting the algorithm autonomously select the instances to undersample and oversample allows us to extend these two successful paradigms to the multilabel task. An extensive comparison setup of 35 datasets shows the advantages of using this approach to deal with class-imbalance datasets for multilabel problems compared with previously published methods as well as the basic classification algorithms with the original datasets.

Antithetic multilevel particle filters

Abstract In this paper we consider the filtering of partially observed multidimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon time-discretization of the diffusion process and then the application of particle filters. Perhaps the state-of-the-art method for moderate-dimensional problems is the multilevel particle filter of Jasra et al. (SIAM J. Numer. Anal.55 (2017), 3068–3096). This is a method that combines multilevel Monte Carlo and particle filters. The approach in that article is based intrinsically upon an Euler discretization method. We develop a new particle filter based upon the antithetic truncated Milstein scheme of Giles and Szpruch (Ann. Appl. Prob.24 (2014), 1585–1620). We show empirically for a class of diffusion problems that, for $\epsilon&gt;0$ given, the cost to produce a mean squared error (MSE) of $\mathcal{O}(\epsilon^2)$ in the estimation of the filter is $\mathcal{O}(\epsilon^{-2}\log(\epsilon)^2)$ . In the case of multidimensional diffusions with non-constant diffusion coefficient, the method of Jasra et al. (2017) requires a cost of $\mathcal{O}(\epsilon^{-2.5})$ to achieve the same MSE.